Jimmy Carter famously "betrayed" many segregationists in his inaugural address - so why didn't this hurt his presidential campaign in the state?

In his inaugural address, Carter famously walked back on his seemingly implied campaign promise of segregation, which he could afford to do, since he only . However, just a few years later, in his 1976 campaign, he won his home by massive margins in both the primary and the general election. Why didn't him walking back his stance on segregation hurt him amongst his constituents and cause many segregationist Democrats to back Wallace in the primaries?